Optical (spectral) data from downhole fluid analysis logging tools are currently used to determine the composition of crude oils downhole. For some tools, the amount of water and carbon-dioxide (CO2) can also be determined. In addition, the optical density can be used to obtain information about asphaltenes and resins.
NMR relaxation and diffusion data can also be used to determine oil composition. From this data, the average carbon chain length and the chain length concentration distribution can be obtained. In addition, the comparison of transverse and longitudinal relaxation times and/or diffusion can give some information about asphaltenes. The shapes of the distributions can be a signal of highly biodegraded oils. Furthermore, the measurement of the NMR relaxation dispersion, i.e., the relaxation profile as a function of the applied magnetic field, can yield additional information about the aggregation propensity of the asphaltenes and resins in the crude oil.
NMR relaxation and diffusion measurements can be made with a downhole fluid analysis logging tool. A combination of factors including tool measurements and the harsh subterranean environment introduce some uncertainty into the calculated relaxation and diffusion distributions. Once the relaxation or diffusion distributions are known, the NMR data can be used to obtain information about chain length distributions and the viscosity of the oil. Several methods have been proposed to relate NMR relaxation and diffusion to chain length distributions. One method makes use of radial basis functions to interpolate between known data and new measurements. Another method uses the constituent viscosity model to relate the diffusion coefficients and relaxation times of each component to its microscopic, or constituent, viscosity. An additional method is based on looking at mixtures of alkanes, but can apply to oils with other components also. Herein, we abbreviate the carbon chain including the carbon length concentration distribution using Cx to indicate a carbon chain of x linear molecules. Carbon chains with components that included carbon branches and/or carbon-carbon double bonds were assumed to have a negligible influence on the final results.
Scaling Law and Fluid Composition Estimation
Previous work estimating fluid composition in terms of component weight fractions has been based on establishing a relationship between component T2 relaxation time and hydrocarbon mixture component chain length. Equation (1) from states that T2,j, the T2 relaxation time for a hydrocarbon mixture component with chain length j, varies as a monomial function of component chain length Nj=j and of harmonic mean chain length N=Σjf(Nj )/Nj where f(Nj) represents the mixture component molar fraction. The constants B, κ, and γ vary with temperature and pressure.T2,j=BNj−κN−γ  (1)
The scaling law (1) has been derived for mixtures of alkanes based on theoretical arguments and limited experimental data of samples. Measurements on dead black oils indicated that this scaling law is also useful for the analysis of crude oils, as long as there is not a lot of asphaltenes present.
Because component T2 relaxation time is a monomial function of chain length in Equation (1), a direct estimate of mean chain length, N, can be computed as a moment of the NMR measurements according to Equation (2).
                              N          _                =                              [                                          B                                                      -                    1                                    /                  k                                            ⁢                              〈                                  T                  2                                      1                    /                    κ                                                  〉                                      ]                                              -              κ                                      γ              +              κ                                                          (        2        )            
Here, terms of the form <T2α> are moments of the T2 distribution that can be computed directly from the NMR measurements using a Mellin transform.
Further, one observes that if T2 relaxation time were a monomial function of chain length Nj=j, then an estimate of fluid viscosity can be made using moments of the T2 distribution as shown in Equation (3).
                              η          ∝                                                    N                _                            β                        ⁢                          〈                              N                v                            〉                                      =                                            [                              〈                                  T                  2                                      1                    /                    κ                                                  〉                            ]                                                                        -                  βκ                                -                                  γ                  ⁢                                                                          ⁢                  v                                                            γ                +                κ                                              ⁢                      〈                          T              2                                                -                  v                                /                κ                                      〉                                              (        3        )            
Estimation of T2 relaxation times from CPMG and GC measurement database
We compiled a database of NMR relaxation (CPMG and T1 T2) and gas chromatography (GC) measurements for oil samples of varying fluid composition taken at a variety of temperatures and pressures. Our initial model for relating CPMG measurements, M(iΔt), to fluid composition in terms of component proton fractions, pj, and component T2 relaxation times, T2,j, is Equation (4).
                              M          ⁡                      (                          i              ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              t                        )                          =                              ∑            i                                                          ⁢                                    p              j              GC                        ⁢                          exp              ⁡                              (                                                      -                    i                                    ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                                      t                    /                                          T                                              2                        ,                        j                                                                                            )                                                                        (        4        )            
Note that proton fractions pjGC can be converted to and from weight fractions by first converting to molar fractions.
Because both GC measurements and NMR measurements are available for each of these crude oil samples in the database, the behavior of component relaxation times T2 as a function of component chain length j can be studied by solving Equation (4) for the component relaxation times T2,j. This non-linear inversion involved making the assumption that (a) we extended the C30+ component of the GC to C30-C60 using a log-linear extension; (b) we assumed a non-increasing behavior of relaxation time T2 as a function of chain length j.
The relaxation times predicted by the scaling law in Equation (1) differ strongly from those predicted using Equation (4). It should be noted that Equation (1) was estimated using a database of oils whose compositions, temperatures, and pressures were much more restricted than those used to invert Equation (4). Further, when a crude oil contains more than about 2 percent of asphaltenes, it was found that Equation (1) systematically overestimates the relaxation times for all components. This is caused by the interaction between the oil molecules and asphaltene that is not considered in Equation (1). In the case of live oils, another limitation is encountered: small molecules such as methane and ethane are not only relaxed by dipolar interaction, but also by the mechanism of spin rotation that is not included in the derivation of Equation (1). For these reasons, Equation (1) also overestimates the relaxation times for molecules of small chain lengths.
Additional analysis using GC and NMR using Carr, Purcell, Meiboom and Gill sequences (CPMG) measurements shows the trend of the relaxation times predicted by Equation (4) roughly follow a log-linear trend and differ strongly from those predicted by the scaling law in Equation (1). Further, the T2 relaxation times estimated using Equation (4) show a dependence on pressure that agrees with our basic NMR physics understanding.
Additional lab data shows the dependence of the T2 relaxation times predicted via Equation (4) for six different oils at a fixed temperature and pressure. The approximate log-linear trends remain in evidence. The dependence on the oil samples, as we shall see, can be shown to be related to arithmetic mean chain length of the oil sample.
We note here that the limitations posed by Equation 1 for the estimation of fluid composition can be overcome by collecting additional diffusion data. Diffusion is intrinsically a more direct probe of the molecular size than relaxation, but is more time consuming to measure. Diffusion measurements allow a much better characterization of the lower chain length compositions, including methane. In addition, a comparison of T1 and T2 measurements allow the detection of asphaltenes. That approach is based on the analysis of NMR relaxation and diffusion measurements using an interpolation scheme within a large data base. A method to resolve these shortcomings is needed.